Scott (1957)
published an important paper on "The Brightest Galaxy in a Cluster as a
Distance
Indicator." Looking back to this study, one may find it contained many basic
points that were later discussed in connection with the Malmquist bias of
the second kind. Her concern was how the availability of a distant cluster
of galaxies influences the use of its brightest galaxy as a standard candle.
Availability means that (a) at least n cluster members
must be brighter than the limiting magnitude m1 of the plate,
and (b) the apparent magnitude of the brightest galaxy must be
brighter than another limit m2, which is needed for
measurements of magnitude and redshift. Let us pick up a few conclusions
of Scott (1957,
p. 249):

(A)t any given distance, a cluster with many members is more likely
to be available to the observer than a cluster containing fewer
galaxies, or

if a very distant cluster is available to the observer, then this
cluster must be unusual, and

the brightest galaxies actually observed in very distant clusters
must have a tendency to possess brighter absolute magnitudes than the
average brightest galaxies in the nearer clusters, hence,

for distant clusters, the simple use of the brightest galaxy in the
cluster
as a distance indicator leads to an underestimate of the distance.

Scott used both numerical simulations and an analytical
model to show the size of systematic errors that the condition of
availability causes to the derived distance at different true distances,
and she concluded
that the selection effect is bound to influence seriously the Hubble m-z
diagram constructed for brightest cluster galaxies. She (1957, p. 264) also
concluded that

an interpretation of the deviations from linearity in the magnitude
redshift
relation that occur near the threshold of available instruments cannot be
made with confidence without appropriate allowance for selection bias.

She (1957, p. 264) also pondered about how to make a
difference between a real and selection-induced deviation from linearity
in the Hubble law:

(T)he question as to whether or not the apparent deviation from
linearity
is an effect of selection [or a real effect] may perhaps be solved by the
accumulation of further data using instruments corresponding to larger
values of both m1 and m2.

Of the above two extracts, Hubble's application is clearly
concerned with the classical Malmquist bias (or Kapteyn's Problem II),
whereas
the discussion by Scott has a relation to Kapteyn's Problem I, though the
effect in galaxy clusters is more complicated. In fact, there is no mention
of the classical Malmquist bias in Scott's paper and really no need for it.